Seems like a "Heddon Hive" would be simpler and you just flip it over every few days...

I don't think the Heddon hive is sold anywhere anymore, and the problem with the Heddon hive is that the parts had to be precision made to ensure that you can flip the boxes over without the frames falling out, while still being able to take the frames out without the bees glueing everything shut. It would take a hardcore hobbyist to remake the Heddon hive.

Varroa mites inside capped cells walk to and fro between the place where they suck on the bee and the place where they lay the eggs. It takes a mite quite a while to knaw a hole in the bee's exoskeleton, so the mite prefers to return to the exact spot where it dug the hole. The mite uses gravity to know where the hole is. If you change the direction of gravity, the mite won't be able to find the hole, so the mite won't have enough nutrition to breed properly. By rotating the brood nest like that, the mites can't breed (so the theory goes).

In theory, swarm cells can't grow in rotating frames, and in theory, bees will store less honey in rotating frames (both these things are also attributes of the Heddon hive, in which the brood section is flipped over every now and then).

Or one with a bit of ingenuity. I would guess I could take a typical box with the frames reasonably tight and roll it (in line with the frames) until it's upside down and it would serve the same basic purpose. Of course that doesn't have the reversible frames, but Heddon's hive had both reversible bodies (with clamps to hold the frames) and reversible frames. I think the reversible frames were way over engineered... but I think a reversible box is less work than engineering a rotating comb...

I would guess I could take a typical box with the frames reasonably tight and roll it (in line with the frames) until it's upside down...

If I understand the theory right, you won't need to turn it upside down. I think it may be sufficient to turn it 90 degrees (in fact, if you turn it 90 degrees to one side, and then 90 degrees to the other side, then you have 180 degrees). Of course, for a 90 degree rotation you'd have to invent a box that's almost as wide as it is high, and find a way to close off the "top" and "bottom" of the box when you've turned it 90 degrees, and find a way to allow bees to move up and down the hive even if the one box was turned 90 degrees.

The advantage of round comb is that you can rotate it without lifting the supers. If you want to "rotate" a box, you'd have to lift the supers every time you turn it.

Manually rotating the brood box won't help with varroa control (from a practical point of view), since varroa mites that successfully mate will lay one female egg every 25-30 hours, [1][2] so you'd have to perform the rotations more than once per day.

The theory is this: For brood, the bees don't care if the cells don't point upwards. However, they can't store a lot of honey in cells that point downwards. This is why the brood nest is made to rotate, but the honey supers aren't. This is also why (if you turn a honey super upside down) the bees will clean out the honey from it and use the cells for brood (this was Heddon's technique: split the brood nest into two shallow boxes, and then flip over the upper box at some stage, which causes the bees to move all its honey to the supers on top, and use the entire upper box for brood).